Quantum traces for representations of surface groups in SL2(ℂ)

Bonahon, Francis¹ ; Wong, Helen²

¹ Department of Mathematics, University of Southern California, 3620 S Vermont Ave, KAP 108, Los Angeles CA 90089-2532, USA
² Department of Mathematics, Carleton College, 1 North College St, Northfield MN 55057, USA

Geometry & topology, Tome 15 (2011) no. 3, pp. 1569-1615.

Résumé

We relate two different quantizations of the character variety consisting of all representations of surface groups in ${SL}_2$. One is the Kauffman skein algebra considered by Bullock, Frohman and Kania-Bartoszyńska, Przytycki and Sikora, and Turaev. The other is the quantum Teichmüller space introduced by Chekhov and Fock and by Kashaev. We construct a homomorphism from the skein algebra to the quantum Teichmüller space which, when restricted to the classical case, corresponds to the equivalence between these two algebras through trace functions.

Détail

DOI : 10.2140/gt.2011.15.1569

Classification : 14D20, 57M25, 57R56
Keywords: Kauffman skein relation, character variety, surface group, skein module, skein algebra, quantum Teichmüller theory

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